I am given the following problem:
Two variables $x$ and $y$ are dependent of $t$ and are related according to
$$y^2-3xy+x^2=25$$
If $x$ varies $1$ unit when $x = 0$ then find $\frac{dy}{dt}$ at that specific moment.
What I have so far is
$$ 2y \frac{dy}{dt} - 3y \frac{dx}{dt} - 3x \frac{dy}{dt} + 2x \frac{dx}{dt} = 0\\ 2y \frac{dy}{dt} - 3y = 0\\ \frac{dy}{dt} = \frac{3}{2} $$
Is that correct? Did I miss something?
Thank you.